Is a double deck game with good rules but only 50% penetration beatable?

Taking your example, if the next card is low, the TC becomes 9.17647... higher. If the next card is 7, 8, or 9, the TC becomes 8.15686... higher. If the next card is high, the TC becomes 7.13725... lower. So the probability it becomes higher is 16/52 + 12/52 = 28/52. The probability it becomes lower is 24/52. P(higher) > P(lower).

But you have to look at the whole distribution -- how much higher/lower and how often -- to get an idea what's happening on average. Why make a mystery out of things that are so easily quantifiable??

ETF

Notice I specifically said 1/2 deck resolution for a "normal" game. There, the TC will not rise if a neutral card comes out, except for once every 26 cards as the next decrease in cards remaining happens...

That was what was "giving me pause" in this discussion.

So we are left with the original assumption (not mine) that the TC is equally probable to go up or down. I don't believe this is quite true after a lot of thought.

The idea that the TC is more likely to drop than rise because there are more big cards than small cards left. (my original idea which I later realized was wrong and started on the current approach that at exact remaining deck resolution, neutral cards also cause the TC to climb).

And finally, what I believe is the _correct_ idea, that for anyone using fractional decks remaining, rather than exact cards remaining, the TC is more likely to drop, because at the 1/2 deck resolution, 25 of 26 times, a neutral card coming out will not affect the TC at all, it will only change 1/26 times when the neutral card is the one that causes us to estimate that now 1/2 deck less remains to be played, causing the TC to rise 1/26 times on neutral cards and remain unchanged 25/26 times on neutral cards. And since we _know_ there are more big cards than small cards, if we ignore neutral cards which tend to leave the TC unchanged, then it would seem that for a "real player" (who uses fractional decks remaining and whole numbers for the TC) that given just the two choices, up or down, the more likely choice is down. If you toss in "no change" then that is by far the winner using fractional decks since many times a change of +/-1 or zero doesn't change the TC at all due to integer math.

Hope that was clearer. But remember the original question, "In a positive true count, is the TC more likely to go up or down?" That's been the question. And the answer is not exactly intuitive at first, based on my admittedly quick analysis. :)

SSR wrote:

Notice I specifically said 1/2 deck resolution for a "normal" game. There, the TC will not rise if a neutral card comes out, except for once every 26 cards as the next decrease in cards remaining happens...

I don�t know you compute your True Counts. For the sake of illustration, let me assume that you round to the nearest half deck. So that if there are 39 cards left, you use 1 deck for your divisor.

If there are 38 cards left, you use 0.5.

Now, at the 39 card point, when a neutral comes out, the TC doubles !

If you compute your divisor some other way, the phenomena will still exist. There will be a critical point where the TC will jump when a neutral card comes out.

You may say that this won�t happen very often. Yes, but when it does happen it has a huge effect. If you average this over all possible positions, you will see that the �average� TC rise will be the same as predicted.

This is really an elementary point. I have watched this thread for some time, and haven�t intervened, because it was such a basic discussion, and the other posters were doing a good job discussing it. But in case you were wondering, I agree with them and not you.

You wrote:

"I don�t know you compute your True Counts. For the sake of illustration, let me assume that you round to the nearest half deck. So that if there are 39 cards left, you use 1 deck for your divisor.

If there are 38 cards left, you use 0.5.

Now, at the 39 card point, when a neutral comes out, the TC doubles ! "

Note that is _exactly_ what I said. I happen to truncate, but at 1/2 deck resolution, there is a point where a neutral card causes the TC to jump. But there are 25 points where a neutral card causes no change. I hope that was clearly in my post you responded to...

The original question, again, was "with a + TC, what is more likely, that the TC will rise or fall?" With exact remaining cards resolution it seems more likely to rise because neutral cards cause the TC to rise, since the denominator shrinks. But at 1/2 deck (normal) deck resolution, this isn't quite the case.

That was my only point...

I am not sure where the "average TC rise" factors in to the question being discussed, which is not about how _much_ the TC will rise or fall, but simply which is more likely (rise or fall only) on a + TC pack...

So, given a + TC, doing 1/2 deck resolution (or any reasonable resolution you want) which is more likely? The TC will rise, or the TC will fall, as the next card hits the felt? Note that "no change" is not a choice...

I originally thought "fall". But then Stealth Bomber made a comment and it got me to thinking. Which led to the current discussion...

Notice I did not say betting without True Count. To bet your money properly you must have a sense of the size of the undealt pack. But you can render the issue of �resolution� of your True Count moot for departure decisions by not employing it.

Suppose you knew how many cards would have to remain unplayed to make your expectation indifferent to whether you made the departure or not. You would then make the departure if fewer than this number remained. You would not make the departure if more than this number remained.

What is this number of cards? It is the ratio formed by dividing the Running Count by the Decision Index. Look at three examples:

#1. Running Count is 9. Decision Index is 3.
RC � DI = 3. Therefore your card quantum of indifference is 3 decks. Depart if fewer than 3 decks remain.

#2. Running Count is 9. Decision Index is 2.
RC � DI = 4�. Your card quantum of indifference is 4� decks. Depart if fewer remain.

#3. Running Count is 9. Decision Index is 4.
RC � DI = 2�. Your card quantum of indifference is 2� decks. Depart if fewer remain.

How does the table of Decision Indices you use define these indices?. Does your table of Departure Indices state that you should depart if the true count is greater than the number in the table? If it does, use the advise as above. Does your table of Departure Indices state that you should depart if the true count is greater than or equal to (GTE) the number in the table? If it does, depart if the ratio and the number of unplayed decks are the same, as the point of indifference is somewhat more than the computed ratio.

Use Wong�s advice of two decades ago. If you are the point of indifference and the pack is negative, you can take the card and expire that pack sooner. If you are the point of indifference and the pack is positive, you can defer taking the card and expire that pack later.

There is more you can do, but you must keep in mind the Law of Diminishing Returns, and focus upon just what it is you wish to accomplish and what it would cost you to accomplish it.

You started out in this subthread by answering somebody elses question, with two statements that were both incorrect, I'm afraid. I was responding to that. Nobody had said anything about half-deck resolution up to that point.

You want half-deck resolution, do the calculation! It isn't hard. But don't pretend the answer can validate your earlier thinking.

Adios,
ETF

> Why do you think that a more-than-average-amount of high cards are more apt to fall soon after the count rises to a high point? If the TC gets to +5, there is just as much chance of the TC getting to +7 as it does to +3. Remember, a +5TC is randomly scatered throughout the remaining pack.<

That was written by Stealth Bomber.

Seems pretty clear that (a) he was talking about a real game, played with a real count, none of which use an exact-card-resolution on the TC that I have seen.

Notice the key statement. "there is just as much chance of the TC getting to +7 (from +5) as it does to +3."

That was where this started. I originally disagreed and thought the probability that the TC would drop was higher in a + count situation. After a couple of posts, he had me thinking, and I realized that (a) with exact-card resolution of the TC, it is actually more likely that the TC will _rise_ because low or neutral cards cause the TC to increase. but (b) with normal resolution (whether it be full deck, half deck or quarter deck doesn't matter) neutral cards will not cause the TC to rise each time one comes out. Because the denominator will only change every N cards, where N is the remaining deck resolution in cards.

I don't believe anything I have written about that is incorrect. With exact card, the TC will rise more often than it will fall due to the neutral card influence. With typical remaining deck resolution, the TC will drop more often than it rises, because there are more big than small cards, making it more likely that a big card will fall before a small card, and since neutrals only affect the TC when we cross a remaining deck boundary, that is not very common.

Again, there is no discussion about how _much_ the TC will rise or fall, there is no discussion about whether it is more likely to rise, fall or stay the same. The discussion was _purely_ about whether it is more likely to rise or fall, period.

Somehow this got side-tracked from what SB, OC from Va and I were originally discussing...

I hope that at least clears up what _I_ was discussing. Along with SB and OCfVA, I can't speak for others of course...

It was an interesting question. I believe my final statement above is the correct answer.

comments???

Yes, I did make an assumption about remaining deck resolution. But since no book I have mentions the concept of exact remaining cards used in TC computations (I have only seen this mentioned in CVCX where it is an option) I chose to ignore the impractical (which gives one result) and take the more usual approach (which gives a different result). Since the original game discussed was 6d/8d, full-deck would have probably been more accurate, but I chose a "worse case" since what works for 1/2 deck accuracy is even more accurate for the 1 deck accuracy since the denominator changes even less frequently making neutral cards affect the TC even less.

Hopefully the end of the story unless you disagree with any of the above, in which case, I'm willing to continue to see where I am wrong...

Which is the reason why I dropped out of the discussion, as it had more or less devolved into meaninglessness.

From a practical point of view, the Step A and Step B post I made earlier is the actual use that is made of both the RC and TC. Any stastical and/or mathematical quirks beyond that have no value as they cannot help you make any additional money.

EXCEPT, possibly, as an answer to a newbie question which appeared a little while ago, namely, "what to do if I lose the count." At that time I put forth the idea that one might simply bet the remainder of the shoe as if the TC was locked at the last known value. I'm not positive this is a good idea, but I'm not sure it's a bad one either. Any thoughts?

A "real game" doesn't use a TC. A real game has a TC. I think it was pretty clear Stealth Bomber was talking about the actual TC, not some mental construct. Why would anyone be concerned about some particular counter's mental state?

Futhermore, x deck resolution is merely a convention used by some software to try to approximate human error. For your argument to have any relevance, even to a counter's mental state, the counter would have to deliberately round to the nearest x deck every time before dividing. A few counters may choose to do this, for some unknown reason, but it is by no means a universal convention.

BTW, the original question was: "Is a double deck game with good rules but only 50% penetration beatable?"

You seem bound and determined to have the last word. Be my guest.

ETF

give me a clue about what your "agenda" is here?

I said: "Seems pretty clear that (a) he was talking about a real game, played with a real count, none of which use an exact-card-resolution on the TC that I have seen." (two posts up from this one).

You replied: "A "real game" doesn't use a TC. A real game has a TC. I think it was pretty clear Stealth Bomber was talking about the actual TC, not some mental construct. Why would anyone be concerned about some particular counter's mental state?"

I don't have any clue about what your reply has to do with my statement. I didn't say "a real game doesn't use a TC". I did say (paraphrased, but exactly quoted above for reference) that a real game uses something _other_ than exact card resolution...

So I suppose I am completely lost as to where you are coming from...

Next, you said "Futhermore, x deck resolution is merely a convention used by some software to try to approximate human error. For your argument to have any relevance, even to a counter's mental state, the counter would have to deliberately round to the nearest x deck every time before dividing. A few counters may choose to do this, for some unknown reason, but it is by no means a universal convention"

I won't presume to speak for "all counters". But the volume of books I have, from the old to the new, _all_ use the partial-deck resolution method. Not a single book I own mentions playing using an exact-remaining-card-count computed true count. Not a single one. And while I don't know hundreds of card counters, I certainly know a few, and not a single one uses this method either. Therefore, I'll stand by my statement above that at least _most_ counters use some rounded/truncated methodology to estimate the remaining cards to be dealt, when they compute the true count. If you don't, more power to you. But it would seem that a majority do not, else all the BJ books I own are suggesting something that nobody is doing. Even CVBJ doesn't offer an exact-card discard tray drill that I can find...

You said "BTW, the original question was: "Is a double deck game with good rules but only 50% penetration beatable?"

I clearly responded to this, which is where this sub-thread started: "This not true. Why do you think that a more-than-average-amount of high cards are more apt to fall soon after the count rises to a high point? If the TC gets to +5, there is just as much chance of the TC getting to +7 as it does to +3. Remember, a +5TC is randomly scatered throughout the remaining pack. " posted by stealth bomber. Why you can't follow that is beyond me.

Finally you said "You seem bound and determined to have the last word. Be my guest."

I would add "you seem bound and determined to ignore the topic being discussed, alter what I wrote in significant ways, all for some reason I do not (and do not want to) understand. I've had great respect for your posts in the past. I'm losing that here...

If you don't want to respond to the topic "with a +5 TC, is the TC more likely to rise or fall as the next card is dealt?" then that is your decision. But please don't try to side-track what I (and two others) were discussing...

If you want to have the last word, at _least_ have the courtesy to have that last word directed to the topic in this sub-thread, not some topic you are manufacturing out of thin air...

I've practiced enough that I don't lose the count, so I'm not quite sure what I would do if I did. I have had to make a quick men's room break, and when I return, I just wait for the shuffle.

For shoe games, to me this seems more practical, since the count can rise or fall, and if it were up when I 'lost it' it might be down when I returned and plopping big bets out seems risky... When I was starting out, if I would get confused about the count, I would try to "deduce" what it is, by recalling the last count I could remember, and asking myself "since then, have I seen more big or small cards, or were they evenly distributed?" If I could answer that, I'd estimate and keep going. If I couldn't, I'd make a men's room run to escape until the next shoe.

Since I hate shoes, and mainly play SD/DD nowadays, I'm not sure what I'd do. Based on the BJ theory of the TC remaining constant over the rest of the shoe, your idea seems reasonable should the need arise...

I shudder to think where this thread will progress to, based on the other one however. :)

So I may be one of the few out there who does not use a set partial deck resolution of the TC.

With so few cards, I find it easy enough to multiply the RC by the reciprocal of the # of decks/partial decks remaining. With enough experience doing that, one eventually gets to the point of just "knowing" the TC without conciously doing the calculations.

Of course, this isn't enough to keep me from being burned from time to time -- always with max bets out, it seems -- by an excess of 7s, 8s & 9s .

about the "no TC conversion necessary after experience". I noticed that "skill" a couple of years ago after lots of play, where with 1.5 decks left, I no longer multiplied by 2/3. I could simply use the running count, the decks left, and "know" the right bet or BS departure. For SD/DD, there just aren't that many different running counts and decks remaining that you can't remember them. :) I deal with 2.0, 1.5, 1.0 and .5 (the latter if it is a really decent game). I can remember to bet 2 units at (these are RC/decks-left pairs) (2,2), (2,1.5), (1,1), four units at (4,2), (3,1.5), (2,1.0) and (1, .5). It is the same "skill" that lets us learn to recognize the value of our hand without adding up individual cards in succession..

l8er

"the likelihood of TC rising in a positive count is the same either way"

I agree if you were talking about a single deck shoe and it also makes sence in theory. But I don't agree if talking about a 6 deck shoe. In theory it DOES make sence what most posters mentioned (only in theory or in a sigle deck). Some might say what's the difference?. Here is my answer: we calculate the TC= RC/approximated N decks. If we were to recalculate the TC after every single neutral comes out, than your statements are correct(same for computer sim)and the TC will rise with more neuts come out, but that's NOT what we do. So for exact calculations based on taking TC counts after every single card comes out(neutral) and the fact that this TC will rise is correct, BUT since we approximate the TC based on the total deck (and not per 1/312 of a 6 deck) then neutrals wouldn't have a noticable affect on the TC count.

that my statements were correct both ways, because I gave both cases. If you calculate TC to exact remaining card resolution, then the TC is more likely to rise than to fall, because the neutral cards being delt increases the TC by decreasing the denominator, where a small card coming out both increases the numerator and decreases the denominator.

But I also clearly said that for those of us that estimate remaining cards to a fraction of a deck, the TC is more likely to drop, because the denominator of the TC conversion fraction stays the same, while the numerator now has a greater probability of dropping because there are more large than small cards remaining.

So practically, the TC is more likely to drop than to rise. But theoretically, at exact remaining cards resolution, it is more likely to rise due to the effect of neutral cards.

Hope I have been clear all the way. I originally answered the "practical way" but then Stealth Bomber commented and got me to thinking (he said it was more likely for the TC to rise than fall in a +TC situation) and when I started thinking about it at the theoretical exact card resolution, lo and behold it is more likely to go up. But as I said, in a "real game" that I (or anyone that I know of) plays, using 1/2 or 1/4 deck resolutions, the TC is more likely to drop due to the truncation effect of integer division...

I think the best way of handling lost count in a shoe is to start over but with more conservative spread till it's done

What difference does it make?